In previous blog post, we have seen simplest example of multiverse. Quilter universe or level I multiverse comes as logical consequence by limits of nature. To far to been reached, but most likely out there. This version of multiverse is sort of an upgrade. Sort of an extension. If you remember or just read previous blog post then you know our cosmic horizon is huge. Beyond the reach it we do not know what exists, but we are sure our patch of universe extends further. How much further we do not know nor does it matter. What certainly is sure is that is huge. What you are about to read discusses things at even grander scale. And its source lies within Big Bang theory. More precisly, within processes which happened at very beginning of time (remember, time did not exist before Big Bang). If this theory is correct, then we have multiple level II universes (kind I will explain in this post) and each of them have at least one (and most likely more) level I universes (as explained in previous post).
I already described what CMB is. It is relic of Universe creation, Big Bang, which is spread across the Universe. It has been discovered by chance and since then it has become important tooling for scientists. It is out window to the past. No matter what advance we may have (based on EM waves), CMB remains oldest thing for us to see (those things before first 370000 years remain trapped in cosmic fog). Calculations show that today there are about 400 million of these cosmic microwave photons racing through every cubic meter of space. Before CMB has been discovered, Big Bang theory has already predicted its existence. Our measurements from Earth show CMB being spread uniformly across the whole Universe we observe. No matter when you measure, you will find leaving distinct signature of 2.725 degrees above absolute zero. It might not be so obvious but the key question here is how can it be so uniform?
Above you see map of the CMB. The different spots of color correspond to different temperatures and in turn, different densities. You may wonder how come now there is different temperature and density if we just said this is uniformly spread? Although the temperature of the CMB is almost completely uniform at 2.7 K, there are very tiny variations, or anisotropies as they are called, in the temperature on the order of 10^-5K. The anisotropies appear on the map as cooler blue and warmer red patches. Ok, so there is this tiny difference, but what does that tell us? These anisotropies correspond to areas of varying density fluctuations in the early universe. Eventually, gravity would draw the high-density fluctuations into even denser and more pronounced ones. After billions of years, these little ripples in the early universe evolved (through gravitational attraction) into the planets, stars, galaxies, and clusters of galaxies as we see it today. OK, so it is sort of uniform then and this variations explain how things started, but they raise the question how did they get so uniform in the first place? What mechanism does stand behind it?
Many people drink coffee (I don't). Maybe better example here would be cup of tea, but it doesn't matter. When served, cup is hot. If you hold it on wrong spot you may get burned. This is because surface of the cup is heated. When objects are in contact, heat migrates from the hotter to the colder, until their temperatures are equal. That's why cup will eventually get to the room temperature for example. In model of Big Bang this fails! Why? Well, for places or objects to reach common temperature there is one essential requirement - mutual contact (direct or through information exchange to correlate it). This exactly why thermos is designed to exactly prevent such interactions. Locations in space that are very far apart. If you look in the sky from north pole you see the first light which managed to reach us on Earth. At the same time you have same situation on south pole. These two distant sources of light never interacted, but however they are uniform.
This brings us to the next puzzle. If light travels at its speed which is limit how come that two objects that used to be close are now so far away? The answer is quite simple though not so well explained by literature. Speed of light is a limit of speed for an object traveling through the space. But expansion we witness today (and since time started) is expansion of space itself. There is no known limit on expansion of space so it may be faster than speed of light. Mathematics of early space (and general relativity) indicates that too. If this is the case, then how could have one object influence other you may ask? In cosmology this is called horizon problem.
Solution to this problem, widely believed and accepted across science community, was given by Alan Guth in 1979. The solution - inflationary cosmology. At the time scientist realized problem was that regions have separated to quickly for thermal equality to happen. The inflationary theory resolves the problem by stating there was a slow speed with which the regions were separating very early on, providing them time to come to the same temperature. It was then, theory proposes, when a brief burst of enormously fast and ever-quickening expansion happened - called inflationary expansion. In such case, uniform conditions we observe no longer pose a mystery, since a common temperature was established before the regions were rapidly driven apart. This is rather hard to grasp as in real life it has to find example for this, right? There is also some sort of gravity which is slowing us down. Einstein established long time ago that gravity comes down from mass, energy and pressure. It is this pressure which is key to the inflation. If you squeeze the ball, while mass remains the same, there is more weight due to the pressure. This has been verified by multiple experiments. The pressure you make in such example is called positive pressure (air pushes outward). Positive pressure contributes to positive gravity (attraction) which leads to increased weight. But pressure can be negative too. In such case, it leads to repulsive gravity (stretched rubber band molecules for example pull inward). OK, so pressure can be negative and gravity can be repulsive, but why would that happen at the Big Bang in the first place? The answer lies in quantum fields.
You probably know what magnetic field is. To refresh our memory, think of magnet above paper clip; clip jumps up and attach itself to magnet. What happened there? Magnet didn't even touch paper clip, but there was still some sort of interaction. This interaction comes from something produced by magnet and called magnetic field. Magnetic field is just one kind of field and as you may have guessed there are more. For example electric field which is responsible for small electric shock I reach the metal doorknob of car sometimes. These two fields are connected; changing one creates another one. Turn on your mobile and place it next to radio or TV and you will hear electromagnetic waves. In second half of 20th century scientists tried to apply EM to microworld of quantum mechanics and this is how quantum field theory was born. With it, we found strong and weak nuclear fields, electron, quark and neutrino fields. There is one field which still remains hypothetical though - inflation field.
We know fields carry energy (eg. magnet to pull paper clip). A field’s value can vary from place to place, but should it be constant, taking the same value everywhere, it would fill space with the same energy at every point. Alan Guth noted such uniform field configurations would not only fill the space with uniform energy but also with uniform negative pressure and that exactly leads to physical mechanism to generate repulsive gravity. Guth also realized value of the field may change thus allowing bursts to happen and stop from happening. If you think of the ball at the top of the hill, you know it has potential energy. When it goes down potential energy is transformed to kinetic one. This is typical. A system harboring potential energy will exploit any opportunity to release that energy. I assume some physicist is responsible for saying "Don't throw away your potential". Same applies to fields and it is described by something called potential energy curve. So, in summary we have inflation field with high potential energy and negative pressure which gives a burst to expansion. As potential energy drops during expansion so does negative pressure. This energy is not lost (as energy level should always be the same); rather it transforms itself into a uniform bath of particles that fill space (think of cooling vat of steam producing water droplets). I won't bother you with numbers here too much, but what math suggests is just outside imaginable; they imply that a region of space the size of a pea would be stretched larger than the observable universe in a time interval so short that the blink of an eye would overestimate it by a factor larger than a million billion billion billion (if you insist on numbers that would be expansion for facto 10^30 within 10^-35 seconds). While these are breath taking figures, they imply thermal equilibrium happened within small space which since has been stretched beyond observable horizon. In inflation, a uniform temperature across space is inevitable.
If above is correct that we have enormous number of level I universes. But this is not what defines level II universe. Today there are many variations of inflationary theories and in many this burst is not one time event. It goes on and on. These theories indicate our universe is just a patch (or hole) in which rapid expansion stopped. And there would be many other out there - all separate areas. This gives birth to Inflationary Multiverse! Inflation field has the same value for each point of space. As it belongs to quantum world, it is subject to quantum uncertainty. This means its value will undergo random quantum jitters. Normally we are not aware of this due to our scale being small and thus they are too small to notice. Nevertheless, calculations show the larger the energy an inflaton has, the greater the fluctuations it will experience from quantum uncertainty (since the inflaton’s energy content during the inflationary burst was extremely high, the jitters in the early universe were big).
What this theory suggests is that we have ever-expanding spatial environment within which bubble universes are created (or pocket universes as they also called). Each of those is huge and one of them is ours. That one, ours, is the one which extends beyond cosmic horizon and which may host multiple level I universes. Same applies to next bubble. And next one. And next one. One way to imagine this it to look at following picture.
Yes, it is Swiss cheese. I love it by the way. Nevertheless, in this case cheese should be seen as spatial dimension carried by inflationary field. Fluctuations result in certain regions to drop from warp speed of expansion and universes as ours form. Those universes are holes in cheese. If inflation theory is correct then the existence of an Inflationary Multiverse would be an inevitable consequence. The number of parallel universes would be simply unimaginable and beyond any number you could think of.
Now let's go back to anisotropies seen on CMB map as briefly discussed before. Even though the observed uniformity of the CMB was one of the prime motivations for developing the inflationary theory, it was realized rapid spatial expansion would not render the radiation perfectly uniform. Instead, it has been argued that quantum mechanical jitters stretched large by the inflationary expansion would overlay the uniformity with minuscule temperature variations, like tiny ripples on the surface of an otherwise smooth pond or lake. Normally, such quantum variations are so tiny and happen over such minuscule scales that they are irrelevant over cosmological distances.
The expansion of space was so rapid, even during the transition out of the inflationary phase, that the microscopic would have been stretched to the macroscopic. Imagine placing a dot or some tiny written message on surface on balloon. Now stretch it. It becomes more visible, right? Same happens here. Tiny fluctuations during this expansion should leave certain signature behind. Calculations show that the temperature differences wouldnt exactly be huge, but could be as large as a thousandth of a degree. If the temperature is 2.725K in one region, the stretched-out quantum jitters would result in its being a touch colder, say 2.7245K, or a touch hotter, 2.7255K, at nearby regions. Scientist around the world were on mission to find this and compare it with what theory has suggested. More impressive, the tiny temperature differences fit a pattern on the sky that is explained spoton by the theoretical calculations. Not impressed? Check it out:
Above graph shows the good agreement of predictions of the inflation theory and observations. The magnitude of temperature variations in the CMB from the early Universe is plotted vertically against the multipole moment. The solid line represents the prediction of the simplest inflationary model and the data points are from satellites and ground-based experiments. Now, that's just fascinating! IMHO this has to be biggest thing cosmology in second part of 20th century if not more (just think of the scale of this whole thing and us as its consequence now figuring out what has happened). Actually, this has been recognized in in 2006 Nobel prize for physics which went to George Smoot and John Mather, who led more than a thousand researchers on the Cosmic Background Explorer team in the early 1990s to the first detection of these temperature differences. Despite all this, having our feet on the ground, inflation field (inflaton) remains hypothetical field and its potential energy curve hasn't been observed. Still, other observations, above included, gives us peace of mind and theorist continue their work on developing existing models.
When we compare this level II universe with previously described level I universe we also see some differences. In level I universe there is no obvious divide between parallel universes. Things simply repeat themselves. In level II universe there is divide. In level I universe we have uniform distribution of content and laws of nature are equal given the circumstances. Values (constants) are same here and in next patch. In level II universe we expect same laws of nature to be present (as they have been created by same process), but constants may be different in value resulting in different aspects of content within each bubble. If Inflationary Multiverse theory is correct is means we not only live in level I (quilted universe), but we are also part of level II universe (bubble or hole in cheese); level I universe exists within level II universe. This also has implication of level I universe; if you had bird perspective level I universe would have spatially finite dimensions.
Credits: Brian Greene, Max Tegmark, Stephen Hawking, Wikipedia